Newton–Lavrentiev regularization of ill-posed Hammerstein type operator equation
In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continu...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
George, S. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Genthiner Strasse 1310875 BerlinGermany: Walter de Gruyter |
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| Anmerkung: |
Copyright 2006, Walter de Gruyter |
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| Umfang: |
10 |
| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Journal of numerical mathematics - Berlin : de Gruyter, 2002, 14, 6, Seite 573-582 |
| Übergeordnetes Werk: |
volume:14 ; number:6 ; pages:573-582 ; extent:10 |
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| DOI / URN: |
10.1515/156939406778474550 |
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NLEJ246224835 |
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| 520 | |a In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. | ||
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10.1515/156939406778474550 doi artikel_Grundlieferung.pp (DE-627)NLEJ246224835 DE-627 ger DE-627 rakwb George, S. verfasserin aut Newton–Lavrentiev regularization of ill-posed Hammerstein type operator equation Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 10 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Walter de Gruyter Online Zeitschriften Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 6, Seite 573-582 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:6 pages:573-582 extent:10 https://doi.org/10.1515/156939406778474550 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 6 573-582 10 |
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10.1515/156939406778474550 doi artikel_Grundlieferung.pp (DE-627)NLEJ246224835 DE-627 ger DE-627 rakwb George, S. verfasserin aut Newton–Lavrentiev regularization of ill-posed Hammerstein type operator equation Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 10 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Walter de Gruyter Online Zeitschriften Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 6, Seite 573-582 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:6 pages:573-582 extent:10 https://doi.org/10.1515/156939406778474550 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 6 573-582 10 |
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10.1515/156939406778474550 doi artikel_Grundlieferung.pp (DE-627)NLEJ246224835 DE-627 ger DE-627 rakwb George, S. verfasserin aut Newton–Lavrentiev regularization of ill-posed Hammerstein type operator equation Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 10 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Walter de Gruyter Online Zeitschriften Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 6, Seite 573-582 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:6 pages:573-582 extent:10 https://doi.org/10.1515/156939406778474550 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 6 573-582 10 |
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10.1515/156939406778474550 doi artikel_Grundlieferung.pp (DE-627)NLEJ246224835 DE-627 ger DE-627 rakwb George, S. verfasserin aut Newton–Lavrentiev regularization of ill-posed Hammerstein type operator equation Genthiner Strasse 1310875 BerlinGermany Walter de Gruyter 10 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Copyright 2006, Walter de Gruyter In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Walter de Gruyter Online Zeitschriften Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 14, 6, Seite 573-582 (DE-627)NLEJ248236172 (DE-600)2095674-5 1569-3953 nnns volume:14 number:6 pages:573-582 extent:10 https://doi.org/10.1515/156939406778474550 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 6 573-582 10 |
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newton–lavrentiev regularization of ill-posed hammerstein type operator equation |
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Newton–Lavrentiev regularization of ill-posed Hammerstein type operator equation |
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In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Copyright 2006, Walter de Gruyter |
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In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Copyright 2006, Walter de Gruyter |
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In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result. Copyright 2006, Walter de Gruyter |
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